1. Should automatically downsample, don't think any settings need adjusting for that, but others can help better(and state your brand and TV model).
2. Only one PS4 can be listed as your primary. This is the console in which your PSN account is tied to. It primarily limits certain PSN elements on your OG console, but all your purchases are still playable just fine on the OG, just use the PSN webstore to download games directly to that console, or log-in on the OG and download from the library. Not certain of all the limitations but others can chime in, but really you can use the backup console just fine outside of some PSN purchasing hoops.
3. Depending on the TV you get there may be a couple settings to activate for 4K and HDR on the TV to get everything to sync properly. GAF can help with this when you do choose and upgrade, but generally most settings will be ready to go and the TV's usually will auto-detect and adjust as necessary. (My Sony 4K set automatically recognizes the PS4 by name and auto switches to Game mode and sets 2160p without my involvement). You mostly just need to make sure to plug the Pro into the proper HDMI port as not all ports are equal on every set(you really just want one that supports HDMI 2.0 and HDCP 2.2 or above...tv documentation will tell you this, or GAF can again tell you once you know the brand and model)